I will go against the flow of reason here and say: you might regret it... if you don't do it.
Life is too short. In no time you will find yourself much older, forever working on other people's crap projects you don't care. It will mean a whole world of difference if you made something for yourself. Even if it failed, who cares, you at least tried.
As a manager, I have almost always approve such requests without much doubt.
I expect to support my team with part time requests.
A team member taking such an initiative is a team member learning a range of things on their own money. Sounds good to me.
Additionally, a positive attitude from me will usually result in the same in return.
Obviously for some ...